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Properties

Label 504.2.ca
Level $504$
Weight $2$
Character orbit 504.ca
Rep. character $\chi_{504}(5,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $184$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.ca (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 504 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(504, [\chi])\).

Total New Old
Modular forms 200 200 0
Cusp forms 184 184 0
Eisenstein series 16 16 0

Trace form

\( 184 q - 2 q^{4} - 6 q^{6} - 2 q^{7} - 2 q^{9} + O(q^{10}) \) \( 184 q - 2 q^{4} - 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} + 12 q^{12} - 18 q^{14} - 2 q^{15} - 2 q^{16} + 12 q^{18} - 6 q^{22} - 6 q^{23} - 12 q^{24} + 78 q^{25} - 6 q^{26} - 8 q^{28} + 7 q^{30} - 6 q^{33} + 6 q^{34} + 22 q^{36} - 33 q^{38} - 8 q^{39} - 18 q^{40} - 42 q^{42} - 9 q^{44} + 2 q^{46} - 12 q^{47} + 9 q^{48} - 2 q^{49} + 9 q^{50} + 21 q^{52} + 33 q^{54} + 18 q^{56} + 4 q^{57} - 3 q^{58} - 59 q^{60} + 12 q^{62} - 72 q^{63} - 8 q^{64} - 42 q^{66} - 18 q^{68} - 27 q^{70} + 12 q^{72} - 12 q^{73} - 57 q^{74} + 12 q^{76} + 19 q^{78} - 4 q^{79} - 57 q^{80} - 18 q^{81} + 69 q^{84} - 27 q^{86} - 6 q^{87} + 9 q^{88} - 24 q^{89} - 75 q^{90} - 36 q^{92} - 45 q^{96} - 45 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(504, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
504.2.ca.a 504.ca 504.ba $184$ $4.024$ None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$